Yes and No.
Keeping an incorrect answer prevents the asker from getting the correct answer as people won't see it in the unanswered queue, so for that reason alone the answer should be removed.
However, there may be times in which a minor error in an answer once pointed out in comments or via an edit makes the answer good enough for the asker.
When someone points out that an answer of mine is wrong I usually delete it. But if it's wrong in an interesting or useful way I edit it to say so and leave it.
Here's one example: Symmetry group of a cube: $O_h \cong O \times C_2$ . I don't know whether it was accepted before or after my edit.
Regarding your question about keeping flawed answers: there are several reasons people delete their answers once a fundamental flaw has been pointed out:
the question will not appear in the Unanswered queue if it has an upvoted incorrect answer, so deleting the flawed approach allows the question to receive more attention;
the answer author may want to fix ...
When you flag an answer as "not an answer" or "very low quality", the answer is pushed into the Low Quality review queue where other users can judge whether in their opinion your flag was justified. In this case, all three reviewers chose the "Looks OK" option, which resulted in your flag being "disputed". After that review, another user flagged the post as "...